A Treatise on Plane and Spherical Trigonometry |
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Page 21
... place to the left : Examples : What number of degrees , minutes , & c . in the English scale correspond to 73 ° , to 71 ° 15 ' , and to 26 ° .0735 , in the French scale . 73 7.3 71.15 7.115 26.0735 2.60735 65.7 64.035 23.46615 6 6 65 ...
... place to the left : Examples : What number of degrees , minutes , & c . in the English scale correspond to 73 ° , to 71 ° 15 ' , and to 26 ° .0735 , in the French scale . 73 7.3 71.15 7.115 26.0735 2.60735 65.7 64.035 23.46615 6 6 65 ...
Page 68
... places of figures , will be .0697989 , conse- quently x or 2 sin . 2o = .0697989 , and sin . 2o = .0346995 . In order to find sin . 1o , take the form ( p . 42 , ) sin . 2A = 2 sin , A. " cos . A , then sin.2 2A = 4 . 68 B) = sin 2 A ...
... places of figures , will be .0697989 , conse- quently x or 2 sin . 2o = .0697989 , and sin . 2o = .0346995 . In order to find sin . 1o , take the form ( p . 42 , ) sin . 2A = 2 sin , A. " cos . A , then sin.2 2A = 4 . 68 B) = sin 2 A ...
Page 69
... places of figures is .0174524 . Repeat the operation , and we have sin . 1 ° 2 > or sin . 30 ' , the value of which is .0087265 . By this method then we have descended from the sin . 30 ° to the sin . 1o and sin . 30 ' ; and ...
... places of figures is .0174524 . Repeat the operation , and we have sin . 1 ° 2 > or sin . 30 ' , the value of which is .0087265 . By this method then we have descended from the sin . 30 ° to the sin . 1o and sin . 30 ' ; and ...
Page 78
... place when the three quantities given are the 3 angles . The reason of the exception is this : take any tri- angle , then , externally or internally , other triangles may be formed with sides parallel to the sides of the proposed ...
... place when the three quantities given are the 3 angles . The reason of the exception is this : take any tri- angle , then , externally or internally , other triangles may be formed with sides parallel to the sides of the proposed ...
Page 89
... places of figures ) would have been doubtful to the extent of 4 " : consequently , for the finding the exact value of C , in this instance , the first method is not proper . * [ C ] [ A ] [ B ] are merely marks of reference . M By the ...
... places of figures ) would have been doubtful to the extent of 4 " : consequently , for the finding the exact value of C , in this instance , the first method is not proper . * [ C ] [ A ] [ B ] are merely marks of reference . M By the ...
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Common terms and phrases
a+b+c analytical arithmetical Asin chord circle circumference co-sec co-tan coefficient compute the sines consequently cos.³ COS.C cosine decimal deduced determined difference equal equation Euclid Example formula fraction given Hence horizontal angle included angle instance latter loga logarithmic sines multiple arcs natural sines nearly oblique oblique-angled obtained plane preceding method Prob PROBLEM Prop quadrant quantity rectilinear triangles required to express right angle right ascension rithm root Rule secant Sherwin's Tables sides similar similarly simple arc sin.² sin.³ sin.c sine and cosine sines of arcs solution spherical angle spherical excess spherical triangle Spherical Trigonometry substitute subtract supplemental triangle tangent Theorem Treatise Trigonometrical formulæ Trigonometrical Survey Trigonometrical Tables versed sine versin
Popular passages
Page 191 - The surface of a spherical triangle is measured by the excess of the sum of its three angles above two right angles, multiplied by the tri-rectangular triangle.
Page 126 - THEOREM. Every section of a sphere, made by a plane, is a circle.
Page 127 - The sum of the three sides of a spherical triangle is less than the circumference of a great circle. Let ABC be any spherical triangle; produce the sides AB, AU, till they meet again in D.
Page 142 - That is, the sines of the sides of a spherical triangle are proportional to the sines of the opposite angles.
Page 125 - A sphere is a solid terminated by a curved surface, all the points of which are equally distant from a point within called the centre.
Page 171 - B . sin c = sin b . sin C cos a = cos b . cos c + sin b . sin c cos b = cos a . cos c + sin a . sin c cos A cos B cos c = cos a . cos b + sin a . sin b . cos C ..2), cotg b . sin c = cos G.
Page 25 - It depends on the principle, that the difference of the squares of two quantities is equal to the product of the sum and difference of the quantities.
Page 138 - ... sun in the meridian. The arches being supposed semi-circular, it is required to find the curve terminating that part of the surface of the water which is illuminated by the sun's rays passing through any arch. 7- It is required to express the cosine of an angle of a spherical triangle in terms of the sines and cosines of the sides.
Page 134 - The measure of the surface of a spherical triangle is the difference between the sum of its three angles and two right angles.
Page 188 - From the logarithm of the area of the triangle, taken as a plane one, in feet, subtract the constant log 9-3267737, then the remainder is the logarithm of the excess above 180°, in seconds nearly.* 3.